Wolfgang Pauli’s Journey Inward

Wolfgang Pauli’s Journey Inward

Men go abroad to wonder at the heights of mountains, at the huge waves of the sea, at the long courses of the rivers, at the vast compass of the ocean, at the circular motions of the stars, and they pass by themselves without wondering.— St. Augustine

When she was little, my daughter Madelynn loved to listen to physics anecdotes; I suppose they served to humanize my somewhat forbidding profession. (Later, in College, she would admit sheepishly that all those years she had believed the word “anecdote” to mean “a story about a physicist.”) By the time she was in high school she knew all about Galileo’s cannon balls, Newton’s apple, and young Einstein’s magnet, but her favorite stories, by a long shot, were about Wolfgang Pauli.

Pauli (1900-1958), who was born in Austria and spent most of his career in Switzerland, was a physicists’ physicist. Although his name is hardly a household word, his role in charting the architecture of the atom, his dramatic prediction of the existence of the elusive neutrino particlethirty-six years before its actual discovery, and his unsurpassed mathematical prowess placed him in the pantheon of physics. He began his career as a prodigy at age nineteen and did not stop calculating (which he called “x-ing”, from the symbol x in algebra) until his premature death of cancer. Along the way he won a Nobel Prize for discovering two fundamental laws of physics and left a treasure trove of about 2500 scientific letters1 published in a massive edition that has been a work in progress for the last twenty-five years. The sheer volume of those letters reflects Pauli’s towering stature in the physics community. His scathing but usually reliable critiques of errors and shoddy workmanship earned him the epithets “The Conscience of Theoretical Physics” among colleagues, and “The Pope of Theoretical Physics” in the press.2

But none of that interested Madelynn. What fascinated and never ceased to delight her was the Pauli effect. Pauli was convinced that he carried an unfortunate aura that doomed experimental apparatus to behave erratically or fail altogether when he was nearby. He believed that a sort of black cloud hovering permanently over his head jinxed any mechanical equipment unlucky enough to be brushed by its penumbra. Although most physicists laughingly dismissed the Pauli effect as a quaint superstition, he himself took it very seriously, and a few of his most illustrious experimental colleagues actually banned him from their laboratories.3

Throughout my career, tales of the mayhem allegedly caused by Pauli’s mere presence have circulated through the physics community by word of mouth. Madelynn’s favorite story concerned Pauli’s visit to Brussels in November of 1948 to attend an international conference.4 The free-spirited Italian experimental physicist Beppo Occhialini, temporarily installed in the city during the difficult aftermath of WWII, set out to tease Pauli with a practical joke. Accordingly, he rigged a hanging lamp in his laboratory to the door in such a manner that it would come crashing to the floor with a great clatter as soon as someone entered. After the mechanism had been connected and tested with care, Pauli, who normally gave laboratories a wide berth, was cajoled into agreeing to a brief visit. When the moment arrived and the great man opened the door, nothing happened.

The story caused Madelynn to melt with glee, no matter how often she heard it.

With casual acquaintances Pauli joked about his mysterious affliction, but close associates knew that to him it was not a laughing matter. It was merely the tip of an iceberg — a visible clue to something much larger and more portentous. The Pauli effect was nothing less than a public hint of irrationality (which he defined to be beyond reason, but not contrary to it)5 in a life that appeared to be dominated by reason. It was the black dot in the white yang, which in turn represents the male in the ancient Chinese yin-yang symbol. In time Pauli came to feel that the irrational component of his personality, represented by the black, female yin, was every bit as significant as its rational counterpart. Pauli called it his shadow and struggled to come to terms with it. What he yearned for was a harmonious balance of yin and yang, of female and male elements, of the irrational and the rational, of soul and body, of religion and science.

During his lifetime, Pauli’s fervent quest for spiritual wholeness was unknown to the public and ignored by his colleagues. Today, with the debate between science and religion once more at high tide, Pauli’s visionary pursuit speaks to us with renewed relevance.

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Wolfgang Pauli was born into the cultural hothouse that was Vienna at the beginning of the twentieth century. His father was a respected university professor of medical chemistry, his mother an accomplished journalist and writer on socialist and feminist themes. In the fertile amalgam of scientific and humanistic cultures to which Pauli was exposed from birth, the most important influence for his future vocation came from his godfather Ernst Mach whose surname is familiar as the unit of supersonic speed. Mach was by then an elder statesman of physics as well as a professor of philosophy and the history of science. Albert Einstein acknowledged that he had been inspired by Mach’s writings, but Pauli enjoyed his influence more directly: Mach encouraged the boy with clever experiments in his home laboratory6 and recommended personal tutors. Pauli, in turn, made the most of his uncommonly rich intellectual environment.

Conventional, organized religion provided what must have been a confusing background for young Pauli’s life. Before he was born, his father, like many other secularized Jews in the increasingly antisemitic Austria, had converted to Catholicism and changed his name from Pascheles to Pauli. His mother, too, was Catholic and had secular Jewish parents, so that by his own reckoning Pauli was three quarters Jewish.7 But as a boy this heritage was assiduously concealed from him. When he was eleven, his parents switched to Protestantism, for unknown reasons, while he and his sister continued to be brought up Catholic. At age sixteen he belatedly learned of his Jewish background, and at twenty-nine, also without giving an explicit reason, he left the Catholic Church.8

In a letter written late in life he explained how these diverse pressures shaped his private beliefs:

“I was always totally cut off from the Jewish spiritual traditions. The Catholic religion, in which I was brought up, was not acceptable to me intellectually (even as a child), but was able to convey to me (regardless of its dogma) what is a rite and what is a ceremony…So I have a Jewish heritage of psychic capabilities, together with a Catholic sense of ritual and ceremony, together with a definite opinion, that the entire ideology of Judeo-Christian monotheism isof no use to me.”9

But in spite of his unequivocal rejection of an anthropomorphic God, Pauli was a deeply spiritual man. If anything, he was ecumenical in his beliefs, taking as much from Pagan and Oriental religions as from the traditions of his childhood. He gave credit to his parents for nurturing his natural skepticism, so that, with his vast erudition, he could pursue his own idiosyncratic spiritual journey through the world’s treasury of philosophical and sacred writings and build his own theology. In this respect, as in his science, Pauli was never a follower, always a creator.

While still in high school Pauli, guided by competent instructors, had learned general relativity, Einstein’s new and notoriously difficult theory of gravity; at age 18 he submitted his first paper on the subject. Upon graduation he enrolled at the University of Munich to study under Arnold Sommerfeld, arguably Europe’s greatest physics teacher. (The list of his students includes an astonishing six Nobel laureates.) But Sommerfeld, although he was an influential role model for Pauli as scientist and as human being, soon reached the limits of the subject matter he could impart to his young pupil, so he assigned him a seemingly impossible task: to write an article on Einstein’s theories of relativity — both the special and the general versions — for the prestigious Encyclopedia of the Mathematical Sciences. The theory of relativity was not only revolutionary, but still largely unfamiliar to the great majority of physicists. The decisive observation of its most unexpected prediction, the bending of starlight by the Sun’s gravity, had just been performed in 1919, a year after Pauli enrolled in university. To entrust this boy just out of high school with a critical review of relativity would seem to be as foolhardy as putting a student pilot in control of a passenger jet.

But Sommerfeld, the consummate teacher, was also an astute judge of talent. In short order Pauli produced an article of over two hundred pages, which instantly became a classic and remained a standard textbook for decades. Upon reading it, Einstein marveled: “No one studying this mature, grandly conceived work would believe that the author is a man of twenty-one.”10 With his lucid and systematic exposition of the history and mathematical development of relativity, not omitting its evolving experimental status, Pauli proved that he was no mere child prodigy. Overnight he became a professional.

It was obvious to experienced observers that Wolfgang Pauli would achieve great things in physics — the only question was when. In the event, they did not have to wait long. At age twenty-four, three years after receiving his doctorate, he proposed two radical ideas that would finally solve the fundamental problem of the structure of the atom, and earn him a Nobel Prize twenty years later. Partly because of their subtlety and partly because of their timing, Pauli’s two papers are overshadowed in popular accounts of the history of physics by the invention of quantum mechanics by his fellow student and close friend Werner Heisenberg six months later. In hindsight, however, the boldness of Pauli’s thinking was nothing short of breathtaking.

The world of physics had been turned on its head in 1900, the year of Pauli’s birth, by the so-called quantum hypothesis, which soon lost its tentative status to become a cornerstone of modern physics. It decrees that in some respects energy, the ubiquitous fuel of the world, resembles water. In bulk it flows a bit like a liquid, but on the atomic scale it consists of tiny discrete bundles called quanta (plural of quantum) — the irreducible constituents of energy. By 1925 this counterintuitive insight had been applied successfully to the explanation of innumerable natural phenomena ranging from light, heat, and electromagnetism to a great variety of chemical transformations, and was beyond dispute. The quantum hypothesis was also capable of clarifying the structure of the atom — with one glaring unresolved discrepancy. Predictably, this shortcoming captured Pauli’s curiosity.

If you confine an electron in a cubical box, three integers account completely for the way its energy is distributed: the number of quanta vested in sideways motion, another number for oscillation up and down, and a number for moving front to back. Thus a single electron might carry two units of energy in the sideways direction, seven up and down, and three back and forth, for a total of twelve units. The three integers, unimaginatively called quantum numbers, correspond to the three dimensions of space, so while the details may differ, the recipe remains the same, no matter what the shape of the box might be. By placing your box between the jaws of a magnet and varying the strength and direction of the magnetic field you can shuffle the quanta around a little bit, but you still need three integers. In the quantum world three numbers describe the motion of a particle in a box.

Since a hydrogen atom resembles a tiny spherical box containing a single electron, a similar analysis furnishes a reasonably accurate model of the atom: three integers specify the motion of the electron. But when you put the atom into a magnetic field, and investigate its properties by watching the light it absorbs and emits, something goes surprisingly wrong: the accounting breaks own. There seem to be more ways to store the energy in the atom than are described by three integers. The name of the phenomenon, the anomalous Zeeman effect, hints at the seriousness of the problem. It cost Pauli two years of agony, which he described to his mentor Sommerfeld: “I examined and rejected a great many hypotheses. But it would just not agree! … I was in complete despair for some time.” Much later he recalled: “A colleague who met me strolling rather aimlessly in the beautiful streets of Copenhagen said to me in a friendly manner, ‘You look very unhappy’; whereupon I answered fiercely, ‘How can one look happy when one is thinking about the anomalous Zeeman effect?’”11

The solution of the puzzle, when he finally hit upon it, was so unorthodox that only a physicist endowed with the most trustworthy intuition and a fertile imagination would dare to propose it. Pauli suggested that an electron, in addition to behaving like a sort of miniature marble meandering through three-dimensional space and carrying energy measured by three integers, actually exists in one of two distinct states. An electron, Pauli claimed, can appear in two different guises that differ from each other in some unfathomable way. Normally it is impossible to tell which of its two forms the particle is exhibiting, because they are so similar, but under very special circumstances — in a magnetic field, for example — the two can have slightly different energies. When that happens, a new quantum number with one of two values, say 0 and 1, is required for counting quanta, in addition to the three conventional ones. In this manner, by inventing a hitherto undiscovered mode of behaviorfor the electron, Pauli solved the enigma of the anomalous Zeeman effect.

It was a wild move. In a way, Pauli broke out of our three everyday dimensions of space into a strange fourth dimension that consists of only two points labeled 0 and 1. He poked his head outside his box, and what he found was a reflection. The electron, it turned out, has its own yin and yang.

Immediately upon hearing this bizarre proposal, the young German-American theoretician Ralph Kronig came up with a simple mechanical interpretation of Pauli’s novel idea.12 The new form of energy, he told Pauli, is invested in the spin of the electron about its own axis, a motion that resembles the daily spin of the Earth, and had never been considered before. The two states of the particle, mirror images as it were, correspond to the difference between clockwise and counterclockwise rotation, which are in turn associated with different energies in a magnetic field. Pauli called the idea “quite clever”, but talked the hapless Kronig out of publishing it, on the grounds that it was too crudely mechanical. In the end, however, Kronig’s view did win the day, though other physicists received credit for it. Today professionals as well as amateurs talk as glibly of the spin of elementary particles as they do of the daily rotation of the Earth — precisely because this type of motion is easily visualized.

Nevertheless, for a number of reasons Pauli was right to call the phenomenon nonmechanical, and to reject Kronig’s proposal. In the first place, the axis of the electron’s spin in a vertical magnetic field can only be aligned in one direction, up and down, not in an arbitrary direction like the spin of a planet. The mechanical equations that describe the Earth’s spin turn out to be totally inadequate for electron spin, and must be replaced by Pauli’s quantum-mechanical formulas. Furthermore, the electron cannot be imagined as a miniature marble, because physicists think of it as a point with no size or spatial extension whatsoever. And though a mathematical point can readily move through three-dimensional space, it can’t conceivably spin. While baseball and golf convincingly display the peculiar behavior of spinning balls,a spinning point is a logical absurdity.

The most significant argument in Pauli’s favor emerged later. His double-valued electron soon became four-valued, and other particles followed suit with their own newly discovered siblings. Although Kronig’s mechanical spin has the advantage over Pauli’s purely abstract conception in its appeal to common sense, similar properties invented later have no analogs in the ordinary world. They go by meaningless names such as the whimsical charm and the nonsensical flavor. Those, in turn, are measured by their own proper quantum numbers, but bear no relation to anything mechanical like spin. With his visionary solution of the Zeeman problem Pauli broke through the walls of our three-dimensional world and steered the thinking of physicists into previously unimagined realms. His version of spin proved to be the model for dealing with a host of new quantum numbers in atomic and nuclear physics, while Kronig’s remained the last link to an earlier time when atomic physics was hamstrung by its slavish reliance on concepts that correspond to everyday experience.

The discovery of spin threatened to exacerbate the already confusing problem of atomic structure. The bewildering collection of ad-hoc rules that had been devised to describe how electrons are arranged in atoms would have to be rewritten to include spin, but before anyone had a chance to begin that difficult project, Pauli untangled the whole mess with a second audacious gambit. The fundamental question had been why the six electrons in the carbon atom, say, don’t all carry the same amount of energy — why their quantum numbers don’t have identical values. Nothing in the way physicists had been taught precluded such an arrangement. On the contrary, it should be expected that the electrons would all seek the same lowest possible energy configuration, the way water seeks the lowest level, and crowd into it. If this rule applied to electrons in atoms, there would be very little difference between, say, carbon with its six and nitrogen with its seven electrons. There would be no chemistry.

Pauli answered the question by decree: the electrons in an atom, he claimed, don’t have the same quantum numbers because they can’t. If one electron is labeled with, say, the four quantum numbers (5, 2, 3, 0) the next electron you add must carry a different label, say (5, 2, 3, 1) or perhaps (6, 2, 3, 0). He proposed no new force between electrons, no mechanism, not even logic to support this injunction. It was simply a rule, imperious in its peremptoriness, and unlike anything else in the entire sweep of modern physics. Electrons avoid each other’s private quantum numbers for no reason other than, as one physicist put it, “for fear of Pauli”.13 His decree is called the Pauli Verbot [Pauli prohibition] in German, and the Exclusion Principle in English. Its only justification is its astonishing explanatory power. With the invention of the fourth quantum number and the exclusion principle Pauli opened the way for the systematic construction of Mendeleev’s entire periodic table. At the price of two daring, albeit unorthodox, assumptions he built a firm physical foundation for the science of chemistry.

By the age of twenty-four Pauli had obtained a teaching position at the university of Hamburg, and arrived at the frontiers of his field. Leaving aside the Pauli effect, which had just begun to rear its spooky head,14 reason seemed to be his lodestar. But buried deep in the editorial apparatus of the eight volumes of his scientific correspondence we come across this chilling footnote:

“It is regrettable that the private correspondence is missing. [Pauli] reports that shortly before his beloved mother’s death [in 1927] he had written her a ‘very cunning [spitzfindig] letter’ in which he explained to her his attitude toward her and his science, which was at the time still purely rational, because he himself considered it a ‘protection, a fortunate circumstance’ that he ‘had no heart and no feelings.’”15

What a devastating phrase “No heart and no feelings”! For all his brilliance, Wolfgang in his twenties was not yet a mature man. But the pain of growing up that is part of the human condition eventually caught up with him. In the four years between the ages of 27 and 31, with his international reputation, sustained by unflagging scientific creativity, at stratospheric heights, several unsettling events occurred in quick succession that finally forced him to look beyond his rational, unfeeling self.

First, the marriage of his parents ends in separation. Then his mother, disappointed in her professional as well as her personal life, commits suicide. His father promptly takes a new wife who is the same age as Pauli. In the following year Pauli imitates his parents by leaving the Catholic Church, and then marries a German nightclub performer. The marriage is shaky from the start and ends in divorce after eleven months. Pauli takes to drink, which gets him thrown out of restaurants and beaten up16, and even leads, during a visit to the University of Michigan, to a broken shoulder. The Pauli effect has turned inward.

During the winter of 1931/32 Pauli, by then professor in Zurich, experienced a psychic crisis which he astutely analyzed three years later in a letter to Ralph Kronig, the inventor of spin, who had become his postdoctoral assistant and personal friend: “I had great fear of everything concerning feeling, and therefore repressed it. This finally caused a revolt against an attitude… that had become too one-sided… Thereby I also became acquainted with psychic matters that I did not know before, which I want to summarize under the phrase Eigent‰tigkeit der Seele [‘the soul acting on its own’ or ‘proper activity of the soul’].” The letter is signed“Your old and new W. Pauli.”17 The man had finally come face to face with his own shadow, the yin of his being.

But contrary to his customary professional independence, he needed help in dealing with his psyche. His father, aware of Pauli’s deteriorating spirits, recommended that he consult Zurich’s most famous psychiatrist, Carl Jung, the apostate disciple of Freud. Jung, in turn, realized that many of Pauli’s difficulties stemmed from his troubles with women, so he referred him to a female pupil. Pauli, with his characteristic love of symmetry and outrageous lack of tact wrote to her:

“I consulted Mr. Jung because of certain neurotic problems which are connected with the fact that it is easier for me to achieve academic success than success with women. Since for Mr. Jung the opposite seems to be the case, he appeared to me to be the appropriate man to treat me medically. To my considerable surprise Mr. Jung explained to me that this was not so, and that I should absolutely have myself treated by a woman.”18

Although the therapy lasted only eight months19, it turned out to be effective: In the following year Pauli felt sufficiently self-confident to enter into a second marriage, which was to last until the end of his life. After the analysis Pauli and Jung began an intense philosophical dialog, and even co-authored a book. While Pauli strove to perceive the world through the lens of reason, Jung believed that human life is dominated by the irrational. The two men inspired each other and agreed that their perspectives were not contradictory, as one might naively assume, but complementary. In psychology and physics they sought the yin and the yang for understanding the world.

That the irrational is an integral part of life is, of course, neither surprising nor particularly remarkable. We all dream, we fall in love, we experience emotions we can’t explain, we believe things we can’t prove, we act without thinking. Our subconscious is constantly at work modifying our thoughts, our feelings, and our actions. Science too, for all its protestations of absolute rationality, is not exempt from the influence of the irrational. Ironically it turns out that it is science at its most sophisticated level, not its most primitive, that is fundamentally dependent on non-rational thinking.

Even Einstein, the consummate rationalist, was fully aware of this dependence. In a letter to a friend he once laid out his view of the scientific method with the help of a little drawing. At the bottom, a horizontal line represents the plane of experience, the everyday world we inhabit and perceive through our senses — the place where all science must of necessity begin and end. High above the plane hovers a point labeled A for axioms: the terse, unprovable mathematical laws that summarize what we know about nature. A stands for propositions such as Newton’s laws of mechanics, Maxwell’s equations of electromagnetism, the laws of thermodynamics, Einstein’s own principles of relativity, and Pauli’s two new rules for the behavior of electrons. From the point A, straight arrows point back down to the plane of experience to represent the strictly logical derivations that theoreticians deduce from the axioms to make predictions, and that experimentalists in turn compare with laboratory observations.

The most remarkable feature of Einstein’s sketch is an exuberant arrow, the only curved line in the drawing, which leads in a swooping arc from just above the plane of experience up to the point A. The arrow does not quite touch the bottom line, because, contrary to naive belief, fundamental laws of science cannot be read off directly from observations or experiments. They are abstractions that are somehow suggested by the direct experiences. The arc represents the inductive part of science that is missing from simple-minded accounts of the scientific method. It describes the work of the handful of truly creative scientists, like Einstein and Pauli, who “freely invent”, as Einstein put it, new concepts for describing the world.

Einstein’s arc may be taken to stand not only for induction, but also for a cluster of other processes, such as intuition, invention, imagination, illumination, innovation, insight, and inspiration, all of which contain a measure of irrationality. For example, no logical or mathematical path leads from the observations of the moon in the sky above an apple falling off a tree to the invention of the law of universal gravitation: only Newton’s imagination, inspired by intuition, was able to achieve that inductive leap. Once the basic principles — Einstein’s “axioms” — have been stated, the road back down to observations is strictly rational, deductive, and much more straightforward, like Einstein’s arrows. Ordinary theoretical physicists like myself spend our careers wresting mathematical consequences from basic principles, and handing the resulting predictions over to our experimental colleagues for comparison with measurements. The basic principles themselves are created by the great geniuses.

When Pauli, who was as nimble at deduction as he was inspired at induction, began to take the irrational side of his psyche more seriously, he began to wonder about how concepts are created in physics. He knew from experience how much more difficult it is to invent new axioms than it is to exploit them. About his discovery of the property that became known as spin he wrote:

“I would like to remark that back in Hamburg my journey to the exclusion principle had to do with just this difficult switch from 3 to 4: namely the necessity of ascribing to the electron, besides its three translations, another, fourth degree of freedom. To struggle through to the understanding that contrary to the naive attitude a fourth quantum number is a property of the same electron — this was actually the principal labor…”20

That, and not the x-ing that he published for all the world to see, was the hard part. Not even Einstein’s unification, twenty years earlier, of the three dimensions of space with the fourth dimension of time had been as radical, because the concept of time was already established then, whereas Pauli had to strike out into altogether unknown territory. “How is that possible?” he asked himself. What hidden wellsprings deep in the human subconscious contribute to this process? Where do new ideas originate? What is the bridge between a scientist’s intuition and the development of scientific concepts and theories?

The problem of the roots of creativity is not confined to science, but applies to art and music and literature as well — in fact to all human activities. It has been much discussed by philosophers and psychologists, and occasionally even by the great creators themselves. A few, such as the philosopher RenÈ Descartes and the chemist Friedrich KekulÈ, described the inevitable invasion of their rational thinking into their waking or sleeping dreams, the realm of the irrational. But no one has pursued the question with as much passion as Pauli.

In order to expose his subconscious processes, his therapist had recommended that he pay attention to his dreams, so he wrote them down methodically and shared them with her and with Jung. Three years after the analysis Jung reported that he had a collection of 1300 Pauli dreams21, a number so astonishing that one scholar suspects that Pauli had already been recording them on his own for several years.22 Be that as it may, Pauli scoured them for references to physics and, not surprisingly, found plenty. (Jung wryly reminded him of the Latin proverb canis panem somniat, piscator pisces — dogs dream of bread, fishermen of fish.)23 At first, such terms as “electric dipole, thermo-electricity, magnetism, atom, electron shells, atomic nucleus, radioactivity”24 seemed to Pauli’s rational mind to be an unjustifiable and idiosyncratic intrusion of scientific terminology into the irrational sphere of dreams, but as the references became more generic and less specific, Pauli started to respect them more. The words that began to turn up in his dreams — doubling, reflection, rotation, revolution, energy, frequency — carry meaning in the everyday language of lay people as well as in physics. They suggested to Pauli that they should be interpreted not only as technical terms, but also as symbols, and that as such they carry a more universal meaning than he had supposed. By following the origins of such terms backward through history to a time when “physical ideas and concepts were still … interspersed with symbolic concepts,”25 including mystical and religious ones, he hoped to find clues to discover the irrational roots of scientific concepts.

The example he chose to study in depth was the work of the German astronomer Johannes Kepler (1571-1630). While Kepler’s fame rests on the mathematical laws with which he described the motions of the planets, his writings are suffused with mystical and religious imagery. Pauli argued that the principal axiom of Kepler’s scheme, the heliocentric model of the universe, was not suggested by the observational evidence at all. Instead, Pauli concluded, Kepler’s belief that the Sun is at the center of things was an expression of religious fervor. The Sun represented God, and its three-dimensional sphere the trinity, so it necessarily assumed a central position. In this way the divine symbol of the Sun formed the bridge Pauli sought between Kepler’s astronomical studies and his mystical beliefs.

Jumping four centuries forward, Pauli then proceeded to analyze the symbols in his own dreams, and their influence on his own scientific creativity. In the course of this investigation he constructed elaborate interpretations of dream images that corresponded directly with his invention of new concepts in physics. For example, he brought his dreams containing references to the magical numbers three and four, with their allusions to the Christian trinity and the Indian mandala, into relation with his discovery of the fourth quantum number.

Throughout Pauli’s career, and ever since, physics has moved steadily away from concrete models (like mechanical spin) and toward the manipulation of symbols that facilitate thinking but bear only an indirect relationship to observable facts. For example, the wave function of quantum mechanics, represented by the Greek letter y, encodes all we know about an atom but has itself only a vague, indistinct, and much debated interpretation. Similarly quarks, the ultimate constituents of matter, are useful symbols, but definitely not things. Physicists may argue about the meaning of y and of quarks, but they all agree on the rules for manipulating the mathematical symbols. In the concept of symbol Pauli thought he had found the missing link between the rational and the irrational, at least as far as physics is concerned.

But the description of the external world was only part of his goal. His inner landscape had become just as important to him. In parallel with his public scientific career he continued to pursue the inward journey that had started with his psychic crisis, and that he had mentioned in his letter to Ralph Kronig. He couldn’t share his insights with most of his colleagues, because they neither understood nor approved. Even Carl Jung, who had launched him on his voyage of discovery, was handicapped by his own lack of understanding of physics. Pauli longed for what he called the “miracle” of finding a companion on his quest — a theoretical physicist who had the requisite human experience and maturity to accompany him.26

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He found his kindred spirit in Markus Fierz (1912 – 2006), his assistant, collaborator, and confidant whom he called his “faithful Eckermann” after Goethe’s famous interlocutor.27 (Full disclosure: Markus Fierz and my father studied physics together in Gˆttingen before WWII and became lifelong friends. Fierz’s twin brother Heiner, whose profession of psychiatry tickled Pauli’s sense of symmetry, was my godfather.) The hundreds of letters the two friends exchanged cover an astonishing range of subjects from theoretical physics to matters historical, philosophical, psychological, spiritual, and religious. Fierz was a prominent physicist himself, widely read, and blessed with an encyclopedic memory. He could hold his own in a dialog with Pauli like few other people on the planet. Nevertheless, since he was ultimately just an ordinary man, his reactions help us to understand the often enigmatic utterances of the truly extraordinary, and often intimidating, Pauli. Their correspondence, which is still largely untranslated into English, opens a tantalizing window on Pauli’s pursuit of his grand vision of “psycho-physical unity.”

In December 1955, after twenty years of professional collaboration and an increasingly close friendship, Pauli finally felt sufficiently self-confident to conduct what he called an experiment: He sent Fierz brief descriptions of several recent dreams and asked him to comment on them. (To put this rather personal request into perspective, it must be noted that in conversations and letters the two men never adopted the familiar German form of address Du, which is used among friends, but always retained the formal, polite Sie.) The year 1955 had brought the death of many friends and relations, including Albert Einstein, Jung’s wife, Fierz’s mother, and Pauli’s father, which exacerbated Pauli’s apprehension of impending old age.28 The defenses he had built around himself since childhood, which had been breached by psychoanalysis, were beginning to crumble.

The timing of this psychological experiment was propitious. Before Fierz had a chance to reply, Pauli embarked on a trip to the Institute for Advanced Study in Princeton, and chose to travel by ship. The ocean voyage, which turned out to be quite turbulent, gave him the opportunity to trade his daily x-ing for more philosophical ruminations. From aboard ship he wrote to Fierz, confessing that he was losing interest in pursuing the scientific questions that had been occupying him at the moment, and felt somewhat untethered. “Whither the voyage?” he asked plaintively. “I have the impression that I only appear to be traveling to the United States.”29 Five weeks later, from Princeton, the question recurs: “Whither my voyage?”

In his reply Fierz reminded Pauli that one of the dreams had dealt explicitly with a voyage, agreed that the trip to America had a special allegorical meaning, and suggested a new project for Pauli. Referring to another one of the dreams, in which a faceless multitude chants “Parle! Parle!” (French for “Speak! Speak!”), he recommended that Pauli should consider embarking upon an attempt to explain the thinking of a modern physicist to the public — not only his uppermost thoughts but also their hidden roots.30 “Many physicists and non-physicists would certainly be very interested in such an account!” he predicted, adding that Pauli’s great prestige would lend authority to his claims, even if they were based more on plausibility than on proof.

The particular question Fierz urged Pauli to address was this:

“In physics we explore nature. Why? In order to dominate it via technology. That’s certainly true; but for you that has never been the motivation. But what is the motivation? One doesn’t discuss this question, because scientists are accustomed to speaking objectively. Scientific objectivity is the cover that enables us not to say what we think. For such thoughts are considered to be subjective, even though all scientists indulge in them, at least in private. Here is the origin of the ‘detached observer’, the scientifically objective observer.”

The ‘detached observer’ was a recurring phrase in Pauli’s vocabulary, and the object of his particular scorn. The term referred to the traditional scientific view of the world as existing “out there”, as it were, with no reference to the observer or the act of observation. Pauli felt that this ideal of absolute detachment was not only philosophically questionable (a full description of the world should include its interactions with the observer), but also physically unattainable. Specifically, he found evidence in modern quantum mechanics to suggest that observers are inextricably entangled with the physical systems they are observing.

As far as Fierz’s suggested project was concerned, Pauli was intrigued. He agreed that domination of nature was indeed not his motivation for doing science, claiming “I know that for me the incentive for reasoning and religious feeling is the same.” (A quarter of a century earlier Einstein had struck a similar note in the New York Times Magazine: “I maintain that the cosmic religious feeling is the strongest and noblest motive for scientific research.”31) But Pauli was never satisfied with the mere observation of a specific personal trait — he was always curious about its underlying general principles. And it so happened, he wrote to Fierz, that a few months earlier he had enunciated just such a generalization in a lecture with the lofty title Science and Western Thought, delivered before an audience of historians.32 The project that would relieve his intellectual malaise could be a popularization of that address.

Pauli asked Fierz to read this lecture and to react to it. It presented European intellectual history as the conflict between two opposing attitudes, called rational-critical and mystical-irrational, respectively. Both attitudes were always present, and “each will always carry the other…within itself as the germ of its contrary.”33 (Although he doesn’t mention it here, the yin-yang symbol can often be perceived hovering in the background of Pauli’s thinking.) The rational-critical worldview is also called science, while mysticism, according to Pauli, is an attitude dominated by the search for unity in the external world, and, ultimately, for unity of the self with the world. Mysticism, on this definition, seeks the redeeming experience of oneness. In Western thought both attitudes have always coexisted, Pauli claimed, whereas in the Orient, where modern science failed to develop, mysticism predominated. In the dialectic between science and mysticism Pauli saw the key for understanding Western thought.

By rehearsing the history of science from Pythagoras through Plato to Kepler, Pauli’s lecture demonstrates that science and mysticism had been closely entwined for more than two thousand years. There was always a balance between the search for rational understanding on the one hand, and the innate desire for redemption or salvation — for deliverance from suffering and evil — on the other. This balance, Pauli proposed, describes not only the way things used to be, but also how they should be, and how he hoped they will be again in the future. It is our destiny, he proclaimed. Unfortunately he found that the advent of modern science in the seventeenth century upset the balance and severed the bond. Today the symmetry between the rational and irrational worldviews is broken, and rationality is running amok. In particular, the ethical foundations of science are called into question in the nuclear age.34

Although Pauli welcomed Fierz’s suggestion of explaining these ideas to the public, he knew that the task would be difficult. The notion that science and religion can be reconciled by means of links such as common symbols — as exemplified by Pauli’s reading of Kepler — sounds far-fetched. Even people who might be expected to be sympathetic to the idea disagreed with it. For example, Pauli’s favorite writer Aldous Huxley, who was enthralled by mysticism, and to whom Pauli had written from Princeton, objected:

“The mystics talk of a state of ‘obscure knowledge’, in which there is an immediate experience of All in one and One in all — of the total presence of the absolute in every relative — of eternity in time — or Nirvana … There is a kind of total omniscience, but no clear knowledge of any particular aspect of the world. The obscure knowledge… does not cast any light on concrete problems…The fact that in Kepler’s case a religious symbol contributed to the working out of a correct scientific hypothesis seems to me, in a sense, accidental.”35

In the face of this blunt rejection Pauli stuck to his guns. “It seems to me that you use the word ‘accidental’ too quickly…” he wrote back. His ace in the hole was the personal experience, which no layman could share, of witnessing the gradual crystallization of a profound insight into nature from a fog of confusion about incomplete and contradictory scientific evidence. “The layman,” he wrote to Huxley, “sees ‘rational clarity’ rather than ‘obscure knowledge’ in science.”36 Pauli knew from a lifetime of painful internal battles, such as his struggle with the anomalous Zeeman effect, what Huxley’s term obscure knowledge actually means to a creator of fundamental new laws.

But in his project of popularization he didn’t advance beyond broad generalities. Earlier he had confessed to Fierz his suspicion that in order find a resolution of the contradictions between science and religion he would have to say “something that would greatly shock both the representatives of conventional religion and the representatives of conventional science. But I do not know exactly what it is.”37 He knew that he would have to break through to a new dimension, just as he had done when he invented spin.

In April 1956 Pauli returned from Princeton to Zurich and to the customary whirlwind of his professional life. Soon he mentioned to Fierz that he had not yet decided to start the project they had discussed. The subject didn’t come up again before his unexpected death two years later.

So Pauli never composed his great sermon on the synthesis of science with religion. But what he privately hoped for emerges from his correspondence with Fierz. He summarily dismissed two extreme attitudes — total separation of science from religion, and complete surrender to mystical experience. The former approach was advocated in our times by the late paleontologist Stephen Jay Gould, who coined the phrase “nonoverlapping magisteria” for the respectful noninterference of the realms of nature and of morality, of what is and what should be.38 Discussing a book by a German physicist who also believed in the separateness of science and religion, Pauli had once written to Fierz that he was appalled, and continuing:

“[The book] is a reversion to the 19th century when religion and science lived in separate sections of the human soul — politely exchanging greetings at a distance, while continually reassuring each other that they had nothing to do with each other — and when the soul seemed to reside outside the boundaries of science.”39

And then Pauli went on to mock the author’s arguments as disingenuous, tired hocus pocus, and weak tea. For Pauli it was obvious that science should be able to deal with the soul, and that the soul in turn informs science.

The other extreme, the mystical self-abandonment to a feeling of unity with the universe, could not possibly be Pauli’s choice either, because it short-circuits science. In fact, he wrote to Fierz, “I believe that such an experience can no longer be achieved properly today, in the age of science, as it could in the past.”40 Instead, Pauli felt, modern scientists must resign themselves to recognizing the contrast between the two competing attitudes, and should strive for their reconciliation. His lecture on Western thought concludes with the idea that such a reconciliation is a goal, “…an aim which includes a synthesis embracing rational understanding as well as the mystic experience of oneness…” Eventually, he hoped, science and religion, which he believed with Einstein to have common roots, will again be one single endeavor, with a common language, common symbols, and a common purpose.

As a model of how this difficult conjunction may be achieved, Pauli proposed the alchemical process. Ignoring as charlatans those who merely attempted to make gold, he focused on the serious few whose quest was as much an exercise in spirituality as in chemistry. They relied on the doctrine of the correspondence between matter and spirit to interpret every physical process in their retorts as a symbol of a transformation in their own souls. The goal was purification: physically it meant the distillation of matter resulting in the philosophers’ stone, and at the same time its spiritual meaning was the refinement of the soul leading to its salvation. The entire process was the magnum opus,the great work. The modern physicist substitutes mathematical theories for the Philosophers’ Stone, and the achievement of self-knowledge for ‘purification of the soul’. Through scientific research into the outside world, and the simultaneous inward journey in search of self, wholeness can be attained. According to Pauli this is the only Heilsweg, which literally means the‘way to salvation’, a term he realized full well is ‘hated by the rationalists’.41

***

The way of the future, Pauli and Fierz agreed, was neither “religion as part of physics”, nor “physics as part of religion,” but the integration of both into a larger, unified enterprise.42 The method of this ambitious, visionary approach to apprehending the world would be scientific, but with due regard for the essential role of irrational processes, which are today suppressed from the scientific dialog. The goal of the enterprise would be nothing less than personal wellbeing or wholeness, which, in a perfect world, would lead to the wellbeing of society. Wholeness has also been called authenticity — it implies being in a good relationship with oneself, with other people, with nature, with the universe. Wholeness includes the self-confidence that comes from self-awareness. It means mental, physical, and spiritual wellbeing.

Pauli’s vision, like many of his scientific ideas, was radical. Not content with establishing religion alongside of science in a harmonious partnership — the commendable aim of many readers of this essay — he wanted more. He demanded the complete fusion of the two. That this union would require changes in science did not give him pause. Pauli, like few others beside him, had helped to introduce profound innovations into physics — radical innovations — modifications that have affected the very nature of the discipline. Thus he had earned the right to call for other, even more far-reaching changes in the future.

The most significant difference between Pauli’s vision and conventional religion lies in their modes of inquiry. By adopting the scientific method, which includes both deduction and induction, the new approach renounces revelation, dogma, and sacred texts as authorities. Knowledge of the soul, like knowledge of the material world, can only be acquired by painstaking and sometimes painful investigation, through hard work — through the opus. Questions replace revealed answers. The search replaces faith as the source of spiritual nourishment.

The primacy of journey over destination, of method over result, in both science and religion, had been advocated before Pauli. For example, Arthur S. Eddington, the pioneering astrophysicist who, like Pauli, had strong mystical leanings but who, as a committed Quaker, belonged to an established church, described his beliefs in similar terms. In his 1929 book Science and the Unseen World he wrote:

“We seek the truth; but if some voice told us that a few years more would see the end of our journey, that the clouds of uncertainty would be dispersed, and that we should perceive the whole truth about the physical universe, the tidings would be by no means joyful. In science as in religion the truth shines ahead as a beacon showing us the path; we do not ask to attain it; it is better far that we be permitted to seek.”43

On Pauli’s journey Markus Fierz served as loyal companion to the end, encouraging, contributing suggestions, and correcting mistakes. But he insisted on registering a crucial caveat. At the end of a long letter to Pauli in Princeton, over fifty years ago, he confessed that he accepted Pauli’s synthesis of science and religion only insofar as it was less a recipe for living in the present than a noble goal for the distant future. Pauli agreed, as witnessed by this passage from one of his letters:

“[Regarding] the great unfinished problem of the relationship between science and religion… I will never get tired of emphasizing that this matter is not finished, that a synthesis of science and religion is necessary, that this problem far exceeds the possibilities of a single person, that this question concerns the development of human consciousness in general, that many changes will still be necessary in both sides (science and religion), before a synthesis of the two will be within the realm of possibility.”44

***

Wolfgang Pauli died fifty years ago, without making much headway in his program. But the goal he so fervidly believed in has not lost its numinous appeal. Short of describing specific steps toward a full unification of science and religion, Pauli’s letters provide pointers in the right direction.

Since science strives for universal validity transcending all ideological boundaries, the same must be true of the eventual unification of science with religion. It follows that the religious component of Pauli’s synthesis cannot depend on any one specific doctrine, but must be conceived much more broadly. One way to achieve this kind of generality is to distinguish belief systems from religious traditions.45 Belief systems are finite, bounded, and limiting, whereas the symbolic power and poetry of the great religions of the world transcend denominational differences. Beliefs answer questions and thereby put an end to thinking, whereas religion, writ large, encourages the limitless, open-ended search for the truth. What Pauli is hinting at is a new, more broadly conceived understanding of religion, freed from encrustations of specific beliefs.

A second lesson Pauli teaches is that we must learn more from quantum mechanics. The Newtonian detached observer, who is passive and aloof from the universe and tries to describe it as it “really is”, cannot deal with the atomic realm. Quantum mechanics shows with increasing clarity and persuasiveness that the way we choose to observe the world shapes what we find — at least to a certain extent. Instead of being detached we are profoundly entangled with the universe. Pauli suspected that most physicists are closet classical thinkers, and have trouble letting go of the beguiling and enduring myth that the world is “out there”, independent of us, detached and “objective”. Before considering the Paulian synthesis, we must therefore work harder to figure out just what it is that quantum mechanics is trying to tell us about the nature of our subtle participation in the unfolding of the world. A small but intrepid band of twenty-first century theorists concerned with the conceptual foundations of physics is, in fact, engaged in this formidable, unfinished task.46

But Pauli’s most lasting legacy is the example of his own life. His scientific discoveries have long since joined the canon of modern physics, whereas his sparse formal writings convey only a fragmentary impression of his worldview. In contrast, his monumental correspondence will continue to bear witness to an inspiring life. Pauli’s life was, in the literal sense of the alchemical opus, a work in progress, defined by the passionate engagement with other people in a relentless search for meaning. It began as a rational quest to understand the physical world, but evolved into a balanced exploration of his universe as well as his own psyche.

To a most unusual degree Wolfgang Pauli managed to integrate the irrational and rational sides of his complex personality, his yin and his yang. So although he did not produce a blueprint for resolving the conflict between science and religion, he did leave to posterity a cornucopia of documentary evidence of his personal voyage of discovery. We can profit by trying to follow in his footsteps.

10 Charles P. Enz No Time to be Brief: A scientific biography of Wolfgang Pauli (Oxford U.P. 2002) [Enz] p.25

11 [Enz] p. 91

12 [Enz] p. 110

13 [Enz] p. 258

14 [Gustafson] p. 200

15 [Briefwechsel] vol. IV part IV B p. 1376

16 [Enz] p. 243

17 [Briefwechsel] vol.II p. 340

18 [Enz] p. 241

19 [Gustafson] p. 187

20 [Gewissen] p. 509

21 [Enz] p. 243

22 [Gustafson] p. 187

23 [Gieser] p. 202

24 [Atom] p. 179

25 [Atom] p. 179

26 [Briefwechsel] vol. IV , part III, p.151

27 [Briefwechsel] vol. IV, part IVA p. 226

28 [Briefwechsel] vol. IV, part III p. 492

29 [Briefwechsel] vol. IV, part III p. 473

30 [Briefwechsel] vol. IV, part III p. 476

31 Albert Einstein Ideas and Opinions (Three Rivers Press 1982) p. 39

32 W. Pauli Writings on Physics and Philosophy (Springer 1994) [Writings] p. 137. (Notice the page number! Pauli would have remarked on it, because he considered 137 to be the most important number in all of physics. It is very close to the measured value of a special, dimensionless combination of three fundamental constants, and is associated with the name of his teacher Sommerfeld. It was also the number of the hospital room in which Pauli died.)

33 [Writings] p. 139

34 [Briefwechsel] vol. IV part III p. 583

35 [Briefwechsel] vol. IV part IV A III p. 655

36 [Briefwechsel] vol. IV part III p. 633

37 [Gieser] p. 255

38 Stephen Jay Gould Rocks of Ages: Science and Religion in the Fullness of Life (Ballentine 1999)

Acknowledgments: For help and encouragement I would like to express my sincere thanks to Marcus Appleby, Chris Fuchs, Bettina Hahne, Preston Moore, Marion Roberts, and my brother Carl von Baeyer. Parts of this essay were written while I was a guest of the Perimeter Institute for Theoretical Physics in Waterloo, Ontario, Canada.